Vortex viscosity in magnetic superconductors due to radiation of spin waves

In type-II superconductors that contain a lattice of magnetic moments, vortices polarize the magnetic system inducing additional contributions to the vortex mass, vortex viscosity, and vortex-vortex interaction. Extra magnetic viscosity is caused by radiation of spin waves by a moving vortex. Like in the case of Cherenkov radiation, this effect has a characteristic threshold behavior and the resulting vortex viscosity may be comparable to the well-known Bardeen-Stephen contribution. The threshold behavior leads to an anomaly in the current-voltage characteristics, and a drop in dissipation for a current interval that is determined by the magnetic excitation spectrum.     

Nuclear magnetic resonance studies of vortices in high temperature superconductors

The distinct distribution of local magnetic fields due to superconducting vortices can be detected with nuclear magnetic resonance (NMR) and used to investigate vortices and related physical properties of extreme type II superconductivity. This review summarizes work on high temperature superconductors (HTS) including cuprates and pnictide materials. Recent experimental results are presented which reveal the nature of vortex matter and novel electronic states. For example, the NMR spectrum has been found to provide a sharp indication of the vortex melting transition. In the vortex solid a frequency dependent spin–lattice relaxation has been reported in cuprates, including YBa₂Cu₃O_7-x, Bi₂SrCa₂Cu₂O_8+δ, and Tl₂Ba₂CuO_6+δ. These results have initiated a new spectroscopy via Doppler shifted nodal quasiparticles for the investigation of vortices. At very high magnetic fields this approach is a promising method for the study of vortex core excitations. These measurements have been used to quantify an induced spin density wave near the vortex cores in Bi₂SrCa₂Cu₂O_8+δ. Although the cuprates have a different superconducting order parameter than the iron arsenide superconductors there are, nonetheless, some striking similarities between them regarding vortex dynamics and frequency dependent relaxation.     

Vortex washboard voltage noise in type-II superconductors

In order to characterize flux flow through disordered type-II superconductors, we investigate the effects of columnar and point defects on the vortex velocity/voltage power spectrum in the driven non-equilibrium steady state. We employ three-dimensional Metropolis Monte Carlo simulations to measure relevant physical observables including the force-velocity/current-voltage (I-V) characteristics, vortex spatial arrangement and structure factor, and mean flux line radius of gyration.Our simulation results compare well to earlier findings and physical intuition.We focus specifically on the voltage noise power spectra in conjunction with the vortex structure factor in the presence of weak columnar and point pinning centers. We investigate the vortex washboard noise peak and associated higher harmonics,and show that the intensity ratios of the washboard harmonics are determined bythe strength of the material defects rather than the type of pins present.Through varying columnar defect lengths and pinning strengths as well as magnetic flux density we further explore the effect of the material defects on vortex transport.It is demonstrated that the radius of gyration displays quantitatively uniquefeatures that depend characteristically on the type of material defects presentin the sample.     

Using μSR to investigate the vortex lattice in high-temperature superconductors

We review some of the properties of the vortex lattice in type II superconductors and the use of muon spin rotation (μSR) to investigate high temperature superconducting oxides. As a microscopic probe of the field distribution inside the bulk of materials, μSR is shown to be a powerful tool with which to study the magnetic properties of superconductors. We also discuss how understanding the complex phenomenology of the vortex lattice in these materials is necessary in order to correctly determine fundamental parameters of the superconducting state.     

Magnetism and disorder effects on muon spin rotation measurements of the magnetic penetration depth in iron-arsenic superconductors

It is shown that attempts to accurately deduce the magnetic penetration depth λ of overdoped BaFe(1.82)Co(0.18)As? single crystals by transverse-field muon spin rotation (TF μSR) are thwarted by field-induced magnetic order and strong vortex-lattice disorder. We explain how substantial deviations from the magnetic field distribution of a nearly perfect vortex lattice by one or both of these factors is also significant for other iron-arsenic superconductors, and this introduces considerable uncertainty in the values of λ obtained by TF μSR.     

Washboard effect of the moving vortex lattice in high-T c superconductors: numerical simulation

Using a simple model of the moving vortex lattice, the washboard effect in the mixed state of high-T _c superconductors, which is due to the interference between the intrinsic oscillation of the vortex lattice and the applied ac driving current, is investigated by numerical simulation. The obtained numerical results are in good agreement with recent experimental measurements on Y BCO crystal [Phys. Rev. Lett. 74, 3684 (1995)]. We also study the case when the ac driving current consists of two frequencies, and observe that the corresponding washboard effect is related not only to the two basic frequencies of the ac current but also to their combination terms.     

Muon spin rotation in heavy-electron pauli-limit superconductors

The formalism for analyzing the magnetic field distribution in the vortex lattice of Pauli-limit heavy-electron superconductors is applied to the evaluation of the vortex lattice static linewidth relevant to the muon spin rotation (??SR) experiment. Based on the Ginzburg-Landau expansion for the superconductor free energy, we study the evolution with respect to the external field of the static linewidth both in the limit of independent vortices (low magnetic field) with a variational expression for the order parameter and in the near H _c2 ^P (T) regime with an extension of the Abrikosov analysis to Pauli-limit superconductors. We conclude that in the Ginzburg-Landau regime in the Pauli-limit, anomalous variations of the static linewidth with the applied field are predicted as a result of the superconductor spin response around a vortex core that dominates the usual charge-response screening supercurrents. We propose the effect as a benchmark for studying new puzzling vortex lattice properties recently observed in CeCoIn₅.     

Magnetic resonance line profile in thin superconducting films

Solutions of the modified London equations are derived for a vortex lattice in a thin film from high-temperature superconductors. The nuclear magnetic resonance line profile in the thin film from high-temperature superconductors of different thicknesses d is calculated with allowance for variable inhomogeneity of the local magnetic field of the vortex lattice. It is demonstrated that the nuclear magnetic resonance line profile changes significantly with d, which can give additional information on the superconductor parameters (including the symmetry type of the vortex lattice and the anisotropy parameter Γ). __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 16–19, November, 2005.     

Resonances, instabilities, and structure selection of driven josephson lattice in layered superconductors

We investigate the dynamics of the Josephson vortex lattice in layered high- T(c) superconductors at high magnetic fields. It is shown that the average electric current depends on the lattice structure and is resonantly enhanced when the Josephson frequency matches the frequency of the plasma mode. We find the stability regions of a moving lattice. It is shown that a specific lattice structure at a given velocity is uniquely selected by the boundary conditions; at small velocities a periodic triangular lattice is stable and looses its stability at some critical velocity. At even higher velocities, a structure close to a rectangular lattice is restored.     

Local magnetic probes of superconductors

Investigations of the magnetic properties of high temperature superconductors (HTSs) have revealed the existence of striking new vortex phenomena due, in part, to their strong crystalline anisotropy, very short coherence lengths and the much larger thermal energies available at high temperatures. Some of these phenomena, for example vortex lattice 'melting', pose serious problems for technological applications of the most anisotropic HTS materials and a fuller understanding of them is of considerable importance. The most direct information regarding vortex structures and dynamics is obtained through local measurement of the magnetic field within or at the surface of a superconducting sample. A detailed review of such local magnetic probes is presented here including Lorentz microscopy, magnetic force microscopy, Bitter decoration, scanning Hall probe microscopy, magneto-optical imaging, and scanning superconducting quantum interference device microscopy. In each case the principles underpinning the technique are described together with the factors that limit the magnetic field and the spatial and temporal resolution. A range of examples will be given, emphasizing applications in the area of HTSs. In addition the ways in which the existing techniques can be expected to develop over the next few years will be discussed and new approaches that seem likely to be successful described.     

On possibility of the spontaneous magnetic flux in a Josephson junction containing magnetic impurities

The Josephson junction containing localized magnetic moments in a dielectric layer between two superconductors is considered. Conditions are studied under which the phase difference between superconductors in the state with energy minimum is equal to π (such a junction we call π-junction). In addition we consider “one-dimensional” Josephson junction one part (2) of which is π-junction, the other (1) being the usual Josephson junction ( 0 - junction). Conditions are found under which in such a system there is a spontaneous vortex with the centre at the boundary between the parts 1 and 2 and magnetic flux associated with this vortex. The vortex appears by second order phase transition as temperature decreases for T_c.     

Vortex liquid crystals in anisotropic type II superconductors

In an isotropic type II superconductor in a moderate magnetic field, the transition to the normal state occurs by vortex lattice melting. In certain anisotropic cases, the vortices acquire elongated cross sections and interactions. Systems of anisotropic, interacting constituents generally exhibit liquid crystalline phases. We examine the possibility of a two step melting in homogeneous type II superconductors with anisotropic superfluid stiffness from a vortex lattice into first a vortex smectic and then a vortex nematic at high temperature and magnetic field. We find that fluctuations of the ordered phase favor an instability to an intermediate smectic-A in the absence of intrinsic pinning.     

Controlling the motion of magnetic flux quanta

We study the transport of vortices in superconductors with triangular arrays of boomerang- or V-shaped asymmetric pinning wells, when applying an alternating electrical current. The asymmetry of the pinning landscape induces a very efficient "diode" effect, that allows the sculpting at will of the magnetic field profile inside the sample. We present the first quantitative study of magnetic "lensing" of fluxons inside superconductors. Our proposed vortex lens provides a near threefold increase of the vortex density at its "focus" regions. The main numerical features have been derived analytically.     

Electromagnetic radiation from vortex flow in Type-II superconductors

We show that a moving vortex lattice, as it comes to a crystal edge, radiates into a free space the harmonics of the washboard frequency, omega(0)=2pi v/a, up to a superconducting gap, Delta/variant Planck's over 2pi. Here v is the velocity of the vortex lattice and a is the intervortex spacing. We compute radiation power and show that this effect can be used for the generation of terahertz radiation and for characterization of moving vortex lattices.     

Vortices in superconducting bulk, films and SQUIDs

The properties of the ideal periodic vortex lattice in bulk superconductors and in films of any thickness can be calculated from Ginzburg-Landau theory by an iteration method using Fourier series. The London theory yields general analytic expressions for the magnetic field and energy of arbitrary arrangements of straight or curved vortex lines. The elasticity of the vortex lattice is highly nonlocal. The magnetic response of superconductors of realistic shapes like thin and thick strips and disks or thin rectangular plates or films, containing pinned vortices, can be computed within continuum theory by solving an integral equation. A useful example is a thin square with a central hole and a radial slit, used as superconducting quantum interference device (SQUID).     

The structure of the vortex lattice in anisotropic superconductors

The structure of the vortex lattice in anisotropic superconductors at an arbitrary temperature in magnetic fields close to critical was studied. Generally, a rhombohedral structure with a vertex angle depending on temperature, magnetic field, and material constants is formed. An important factor is the small (2%) difference of the free energies of the triangular and square lattices in the Ginzburg-Landau approximation. This factor also persists in anisotropic superconductors.     

Formation of multiple-flux-quantum vortices in mesoscopic superconductors from simulations of calorimetric, magnetic, and transport properties

Because of strong flux confinement in mesoscopic superconductors, a "giant" vortex may appear in the ground state of the system in an applied magnetic field. This multiquanta vortex can then split into individual vortices (and vice versa) as a function of, e.g., applied current, magnetic field, or temperature. Here we show that such transitions can be identified by calorimetry, as the formation or splitting of a giant vortex results in a clear jump in measured heat capacity versus external drive. We attribute this phenomenon to an abrupt change in the density of states of the quasiparticle excitations in the vortex core(s), and further link it to a sharp change of the magnetic susceptibility at the transition--proving that the formation of a giant vortex can also be detected by magnetometry.     

Low energy spin waves and magnetic interactions in SrFe2As2

We report inelastic neutron scattering studies of magnetic excitations in antiferromagnetically ordered SrFe2As2 (T_{N}=200-220 K), the parent compound of the FeAs-based superconductors. At low temperatures (T=7 K), the magnetic spectrum S(Q,Planck's omega) consists of a Bragg peak at the elastic position (Planck's omega=0 meV), a spin gap (Delta< or =6.5 meV), and sharp spin-wave excitations at higher energies. Based on the observed dispersion relation, we estimate the effective magnetic exchange coupling using a Heisenberg model. On warming across T_{N}, the low-temperature spin gap rapidly closes, with weak critical scattering and spin-spin correlations in the paramagnetic state. The antiferromagnetic order in SrFe2As2 is therefore consistent with a first order phase transition, similar to the structural lattice distortion.     

What does NMR tell us about the electronic state of high-T c superconductors?

An introduction to the models which are usually applied, when interpreting the NMR (nuclear magnetic resonance) parameter Knight shift (K _s) and spin-lattice relaxation rate 1/T ₁ in the normal and the superconducting state of high-temperature superconductors, is given. The different hyperfine interaction parameters involved, as well as the static and dynamic susceptibility χ(q,ω) will be discussed. I will point at those highlights as antiferromagnetic correlations, spin gap and vortex lattice dynamics which have emerged from the analysis of the NMR data.     

Spin configurations in nanostructured magnetic rings: From DC transport to GHz spectroscopy

We report three different experiments performed on permalloy nanorings. They address either (a) the stray-field and (b) the magnetoresistance characteristics of an individual nanoring, or (c) the magnetization dynamics of a periodic array of identical rings. Interestingly, in all three properties covering the frequency range from DC to 20 GHz we observe irreversible switching and hysteretic behavior. Localized spin waves, which are excited by ferromagnetic resonance in different ring segments, are found to obey an intriguing magnetic field dispersion. We attribute this to the characteristic spin configurations in the nanorings, i.e., the onion and the vortex states, which are controlled by the external magnetic field.